Differentiate a vector-valued function

Definition

Differentiating a vector-valued function involves finding the derivative of each component of the vector separately. It measures how the vector changes with respect to its independent variable.

Analogy

Think of a group of friends walking together in a park. Each friend represents a component of the vector, and differentiating the vector-valued function is like observing how each friend's position changes as they walk.

Related terms

Tangent Vector: A tangent vector represents the instantaneous rate of change or velocity at any given point on a curve.

Chain Rule for Vector-Valued Functions: The chain rule allows us to find derivatives of composite functions involving vectors.

Parametric Equations: Parametric equations describe curves by expressing coordinates as functions of an independent parameter.